Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs

DOI10.1007/978-1-4614-5128-0_2zbMath1269.05077OpenAlexW1948893736WikidataQ57908690 ScholiaQ57908690MaRDI QIDQ2841696

Elias P. Tsigaridas, Ioannis Z. Emiris, Antonios Varvitsiotis

Publication date: 29 July 2013

Published in: Distance Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-5128-0_2

zbMATH Keywords

mixed volumepolynomial systemEuclidean embeddingrigid graphHenneberg constructionLaman graphCayley-Menger matrixcyclohexane caterpillar

Mathematics Subject Classification ID

Applications of graph theory (05C90) General theory of distance geometry (51K05) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (9)

The m-Bézout bound and distance geometry ⋮ The Number of Realizations of a Laman Graph ⋮ New upper bounds for the number of embeddings of minimally rigid graphs ⋮ Counting realizations of Laman graphs on the sphere ⋮ Computing the number of realizations of a Laman graph ⋮ Lower Bounds on the Number of Realizations of Rigid Graphs ⋮ On the maximal number of real embeddings of minimally rigid graphs in \(\mathbb{R}^2,\mathbb{R}^3\) and \(S^2\) ⋮ Equivalent realisations of a rigid graph ⋮ On the multihomogeneous Bézout bound on the number of embeddings of minimally rigid graphs

Uses Software

• PHCpack
• DYANA

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